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General boundary conditions ("branes") for the Poisson sigma model arestudied. They turn out to be labeled by coisotropic submanifolds of the givenPoisson manifold. The role played by these boundary conditions both at theclassical and at the perturbative quantum level is discussed. It turns out tobe related at the classical level to the category of Poisson manifolds withdual pairs as morphisms and at the perturbative quantum level to the categoryof associative algebras (deforming algebras of functions on Poisson manifolds)with bimodules as morphisms. Possibly singular Poisson manifolds arising fromreduction enter naturally into the picture and, in particular, the constructionyields (under certain assumptions) their deformation quantization.Comment: 21 pages, 2 figures; minor corrections, references updated; final  versio

Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model